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Restricted confidence intervals for ordered binary and survival data

Cuddy, Rich (2019) Restricted confidence intervals for ordered binary and survival data. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

This paper considers restricted confidence intervals for binary and survival data with simple ordering. An example in a cancer clinical trial is that we expect patients with a lower stage of cancer to have higher progression free or overall survival rates at all times than those with a higher stage. This type of information is often neglected by Public Health investigators, while appropriately incorporating this information may significantly improve the efficiency in the estimators of interest. When data are normally distributed, a method has been proposed to construct restricted confidence intervals. The process is done by first identifying intermediate variables between two observations, optimizing based on the new parameter space, and then modifying the confidence interval upper and lower bounds using confidence interval limits for the intermediate random variables. In this paper, we explore and extend this method to binary data and survival data. Simulation study shows that the proposed restricted confidence intervals preserve the coverage rate well by closing to the nominal level, even when the sample size is small. The reduction of confidence interval lengths is significant when the underlying true parameters are close to each other, particularly for those with smaller sample sizes.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Cuddy, Richrjc77@pitt.edurjc77
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairPark, Yongseok
Committee MemberKang, Chaeryon
Committee MemberT.A. Marques Jr, Ernesto
Date: 26 September 2019
Date Type: Publication
Defense Date: 29 July 2019
Approval Date: 26 September 2019
Submission Date: 23 July 2019
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 21
Institution: University of Pittsburgh
Schools and Programs: School of Public Health > Biostatistics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: Binomial distribution, Kaplan-Meier Estimator, Ordered Statistics, Restricted Confidence Interval
Date Deposited: 26 Sep 2019 16:53
Last Modified: 27 Sep 2019 18:11
URI: http://d-scholarship.pitt.edu/id/eprint/37363

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